I think all state parks have electric hookups, at the very least. Some have water hook ups as well, if not there are water faucets located in several different places throughout the campgrounds. I'm not sure if any have sewer hookups but they do have dump stations. Now state forest campgrounds are rustic, no electric, and no water hookups, just water faucets probably near the vault type toilets. Regular state parks have very nice bathrooms, and individual showers. Usually the campsites are quite large too, and we love the ones that have trees/bushes separating the sites.
Yes, you do need to get to Michigan!
It's a very beautiful area with lots to see and do, and several waterfalls besides Tahquamenon, and lighthouses as well. The upper falls are pretty majestic, and beautiful. The lower falls has an island and you can rent a rowboat (last time we went I think it was $2) to go over to the island and walk around it, really nice. There is also a trail connecting the upper and lower falls and we walked that once, it was fun.
We finally went in the winter a few years ago and it was awesome to see the falls frozen over. There were few people, and it was lightly snowing when we were there, so pretty and so different from summer. Autumn is a great time to go, less busy (kids back in school) and the colors are amazing.
The Rivermouth campground has two campgrounds, one is modern with electric and water, bathrooms with showers, etc. and the other side is the rustic side with no electric, water faucets here and there, and vault toilets. But you can walk over to the modern campground and take showers. It is just so beautiful and peaceful right on the river so we prefer the rustic side.